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Classification: Decision Trees

Classification: Decision Trees. Classification: Definition. Given a collection of records ( training set ) Each record contains a set of attributes , one of the attributes is the class . Find a model for class attribute as a function of the values of other attributes.

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Classification: Decision Trees

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  1. Classification: Decision Trees

  2. Classification: Definition • Given a collection of records (training set ) • Each record contains a set of attributes, one of the attributes is the class. • Find a model for class attribute as a function of the values of other attributes. • Goal: previously unseen records should be assigned a class as accurately as possible. • A test set is used to determine the accuracy of the model. Usually, the given data set is divided into training and test sets, with training set used to build the model and test set used to validate it.

  3. Classification—A Two-Step Process • Model construction: describing a set of predetermined classes • Each tuple/sample is assumed to belong to a predefined class, as determined by the class label attribute • The set of tuples used for model construction: training set • The model is represented as classification rules, decision trees, or mathematical formulae • Model usage: for classifying future or unknown objects • Estimate accuracy of the model • The known label of test sample is compared with the classified result from the model • Accuracy rate is the percentage of test set samples that are correctly classified by the model • Test set is independent of training set, otherwise over-fitting will occur

  4. Training Data Classifier (Model) Classification Process (1): Model Construction Classification Algorithms IF rank = ‘professor’ OR years > 6 THEN tenured = ‘yes’

  5. Classifier Testing Data Unseen Data Classification Process (2): Use the Model in Prediction (Jeff, Professor, 4) Tenured?

  6. Illustrating Classification Task

  7. Examples of Classification Task • Predicting tumor cells as benign or malignant • Classifying credit card transactions as legitimate or fraudulent • Classifying secondary structures of protein as alpha-helix, beta-sheet, or random coil • Categorizing news stories as finance, weather, entertainment, sports, etc

  8. Classification Techniques • Decision Tree based Methods • Rule-based Methods • Memory based reasoning • Neural Networks • Naïve Bayes and Bayesian Belief Networks • Support Vector Machines

  9. categorical categorical continuous class Example of a Decision Tree Splitting Attributes Refund Yes No NO MarSt Married Single, Divorced TaxInc NO < 80K > 80K YES NO Model: Decision Tree Training Data

  10. NO Another Example of Decision Tree categorical categorical continuous class Single, Divorced MarSt Married NO Refund No Yes TaxInc < 80K > 80K YES NO There could be more than one tree that fits the same data!

  11. Decision Tree Classification Task Decision Tree

  12. Refund Yes No NO MarSt Married Single, Divorced TaxInc NO < 80K > 80K YES NO Apply Model to Test Data Test Data Start from the root of tree.

  13. Refund Yes No NO MarSt Married Single, Divorced TaxInc NO < 80K > 80K YES NO Apply Model to Test Data Test Data

  14. Apply Model to Test Data Test Data Refund Yes No NO MarSt Married Single, Divorced TaxInc NO < 80K > 80K YES NO

  15. Apply Model to Test Data Test Data Refund Yes No NO MarSt Married Single, Divorced TaxInc NO < 80K > 80K YES NO

  16. Apply Model to Test Data Test Data Refund Yes No NO MarSt Married Single, Divorced TaxInc NO < 80K > 80K YES NO

  17. Apply Model to Test Data Test Data Refund Yes No NO MarSt Assign Cheat to “No” Married Single, Divorced TaxInc NO < 80K > 80K YES NO

  18. Decision Tree Classification Task Decision Tree

  19. Outline • Top-Down Decision Tree Construction • Choosing the Splitting Attribute • Information Gain and Gain Ratio

  20. DECISION TREE • An internal node is a test on an attribute. • A branch represents an outcome of the test, e.g., Color=red. • A leaf node represents a class label or class label distribution. • At each node, one attribute is chosen to split training examples into distinct classes as much as possible • A new case is classified by following a matching path to a leaf node.

  21. Weather Data: Play or not Play? Note: Outlook is the Forecast, no relation to Microsoft email program

  22. Example Tree for “Play?” Outlook sunny rain overcast Yes Humidity Windy high normal false true No Yes No Yes

  23. Building Decision Tree [Q93] • Top-down tree construction • At start, all training examples are at the root. • Partition the examples recursively by choosing one attribute each time. • Bottom-up tree pruning • Remove subtrees or branches, in a bottom-up manner, to improve the estimated accuracy on new cases.

  24. Choosing the Splitting Attribute • At each node, available attributes are evaluated on the basis of separating the classes of the training examples. A Goodness function is used for this purpose. • Typical goodness functions: • information gain (ID3/C4.5) • information gain ratio • gini index witten&eibe

  25. How to determine the Best Split • Greedy approach: • Nodes with homogeneous class distribution are preferred • Need a measure of node impurity: Non-homogeneous, High degree of impurity Homogeneous, Low degree of impurity

  26. Splitting Criteria based on INFO • Entropy at a given node t: (NOTE: p( j | t) is the relative frequency of class j at node t). • Measures homogeneity of a node. • Maximum (log nc) when records are equally distributed among all classes implying least information • Minimum (0.0) when all records belong to one class, implying most information • Entropy based computations are similar to the GINI index computations

  27. Examples for computing Entropy P(C1) = 0/6 = 0 P(C2) = 6/6 = 1 Entropy = – 0 log 0– 1 log 1 = – 0 – 0 = 0 P(C1) = 1/6 P(C2) = 5/6 Entropy = – (1/6) log2 (1/6)– (5/6) log2 (1/6) = 0.65 P(C1) = 2/6 P(C2) = 4/6 Entropy = – (2/6) log2 (2/6)– (4/6) log2 (4/6) = 0.92

  28. Splitting Based on INFO... • Information Gain: Parent Node, p is split into k partitions; ni is number of records in partition i • Measures Reduction in Entropy achieved because of the split. Choose the split that achieves most reduction (maximizes GAIN) • Used in ID3 and C4.5 • Disadvantage: Tends to prefer splits that result in large number of partitions, each being small but pure.

  29. Which attribute to select? witten&eibe

  30. A criterion for attribute selection • Which is the best attribute? • The one which will result in the smallest tree • Heuristic: choose the attribute that produces the “purest” nodes • Popular impurity criterion: information gain • Information gain increases with the average purity of the subsets that an attribute produces • Strategy: choose attribute that results in greatest information gain witten&eibe

  31. Example: attribute “Outlook” • “Outlook” = “Sunny”: • “Outlook” = “Overcast”: • “Outlook” = “Rainy”: • Expected information for attribute: Note: log(0) is not defined, but we evaluate 0*log(0) as zero witten&eibe

  32. Computing the information gain • Information gain: (information before split) – (information after split) • Information gain for attributes from weather data: witten&eibe

  33. Continuing to split witten&eibe

  34. The final decision tree • Note: not all leaves need to be pure; sometimes identical instances have different classes  Splitting stops when data can’t be split any further witten&eibe

  35. Gini Index • If a data set T contains examples from n classes, gini index, gini(T) is defined as where pj is the relative frequency of class j in T. • If a data set T is split into two subsets T1 and T2 with sizes N1 and N2 respectively, the gini index of the split data contains examples from n classes, the gini index gini(T) is defined as • The attribute provides the smallest ginisplit(T) is chosen to split the node (need to enumerate all possible splitting points for each attribute).

  36. Measure of Impurity: GINI • Gini Index for a given node t : (NOTE: p( j | t) is the relative frequency of class j at node t). • Maximum (1 - 1/nc) when records are equally distributed among all classes, implying least interesting information • Minimum (0.0) when all records belong to one class, implying most interesting information

  37. Examples for computing GINI P(C1) = 0/6 = 0 P(C2) = 6/6 = 1 Gini = 1 – P(C1)2 – P(C2)2 = 1 – 0 – 1 = 0 P(C1) = 1/6 P(C2) = 5/6 Gini = 1 – (1/6)2 – (5/6)2 = 0.278 P(C1) = 2/6 P(C2) = 4/6 Gini = 1 – (2/6)2 – (4/6)2 = 0.444

  38. Stopping Criteria for Tree Induction • Stop expanding a node when all the records belong to the same class • Stop expanding a node when all the records have similar attribute values • Early termination (to be discussed later)

  39. Decision Tree Based Classification • Advantages: • Inexpensive to construct • Extremely fast at classifying unknown records • Easy to interpret for small-sized trees • Accuracy is comparable to other classification techniques for many simple data sets

  40. Example: C4.5 • Simple depth-first construction. • Uses Information Gain • Sorts Continuous Attributes at each node. • Needs entire data to fit in memory. • Unsuitable for Large Datasets. • Needs out-of-core sorting. • You can download the software from:http://www.cse.unsw.edu.au/~quinlan/c4.5r8.tar.gz

  41. Practical Issues of Classification • Underfitting and Overfitting • Missing Values • Costs of Classification

  42. Underfitting and Overfitting Overfitting Underfitting: when model is too simple, both training and test errors are large

  43. Overfitting due to Noise Decision boundary is distorted by noise point

  44. Overfitting due to Insufficient Examples Lack of data points in the lower half of the diagram makes it difficult to predict correctly the class labels of that region - Insufficient number of training records in the region causes the decision tree to predict the test examples using other training records that are irrelevant to the classification task

  45. Notes on Overfitting • Overfitting results in decision trees that are more complex than necessary • Training error no longer provides a good estimate of how well the tree will perform on previously unseen records • Need new ways for estimating errors

  46. Model Evaluation • Metrics for Performance Evaluation • How to evaluate the performance of a model? • Methods for Performance Evaluation • How to obtain reliable estimates? • Methods for Model Comparison • How to compare the relative performance among competing models?

  47. Model Evaluation • Metrics for Performance Evaluation • How to evaluate the performance of a model? • Methods for Performance Evaluation • How to obtain reliable estimates? • Methods for Model Comparison • How to compare the relative performance among competing models?

  48. Metrics for Performance Evaluation • Focus on the predictive capability of a model • Rather than how fast it takes to classify or build models, scalability, etc. • Confusion Matrix: a: TP (true positive) b: FN (false negative) c: FP (false positive) d: TN (true negative)

  49. Metrics for Performance Evaluation… • Most widely-used metric:

  50. Limitation of Accuracy • Consider a 2-class problem • Number of Class 0 examples = 9990 • Number of Class 1 examples = 10 • If model predicts everything to be class 0, accuracy is 9990/10000 = 99.9 % • Accuracy is misleading because model does not detect any class 1 example

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